Page 116 - handbook 20152016

Faculty of Science Handbook, Session 2015/2016

Assessment: Life Annuities: continuous type life annuities, discrete type
Continuous Assessment: 40% life annuities, expectation and variance, probabilities,
Final Examination: 60% percentiles, recursive formulas, m-thly payments, varying
annuities.
Medium of Instruction:
English Premiums: expectation and variance of loss random
variable, fully continuous and discrete premiums,
Humanity Skill: semicontinuous premiums, m-thly premiums, gross
CS3, CT3 premiums, probabilities, percentiles.

References: Assessment:
1. Broverman, S. A. (2010). Mathematics of investment Continuous Assessment: 40%
and credit, 5th Ed., Actex Publications. Final Examination: 60%
2. Kellison, G. (2008). Theory of Interest, 3rd Ed.,
McGraw-Hill. Medium of Instruction:
3. McDonald, R. L. (2012). Derivatives markets, 3rd Ed., English
Prentice Hall.
4. McCutcheon, J.J., Scott W.F.(1989). Introduction to Humanity Skill:
the Mathematics of Finance, Butterworth-Heinemann. CS3, CT3

References:
1. Bowers, N., Gerber, H., Hickman, J., Jones, D.,
SIQ2004 SURVIVAL MODEL Nesbitt, C. (1997). Actuarial mathematics, 2nd ed.,
Society of Actuaries.
Estimation of lifetime distributions: lifetime distributions, 2. Dickson, D. C., Hardy, M. R., & Waters, H. R. (2013).
cohort studies, censoring, Kaplan-Meier estimates, Cox Actuarial mathematics for life contingent risks.
regression model and its estimation. Cambridge University Press.
3. Cunningham, R. J. (2011). Models for quantifying risk.
Markov models: Multi-state Markov models, Kolmogorov Actex Publications.
forward equations, estimation of the force of mortality, 4. Promislow, S. D. (2011). Fundamentals of actuarial
estimation of multi-state model transition intensities. mathematics. John Wiley & Sons.

Binomial and Poisson models of mortality: Binomial model
of mortality, uniform and constant force of mortality
assumptions, maximum likelihood estimator for the rate of SIQ3002 PORTFOLIO THEORY AND ASSET MODELS
mortality, Poisson models.
Utility theory: Features of utility functions, expected utility
Graduation and statistical tests: methods of graduating theorem, risk aversion.
crude estimates, Chi-square test, standardised deviation
test, sign test, grouping of sign test, serial correlations test. Stochastic dominance: Absolute, first and second order
stochastic dominance.
Exposed to risk: Exact exposed to risk, approximate
exposed to risk using census data. Measures of investment risk: Variance, semi-variance,
probability of shortfall, value-at-risk, expected shortfall.
Assessment:
Continuous Assessment: 40% Portfolio theory: Mean-variance portfolio, diversification,
Final Examination: 60% efficient frontier, optimal portfolio selection, efficient
portfolio identification.
Medium of Instruction:
English Models of asset returns: Single-index models, fitting a
single index model, multi-index models.
Humanity Skill:
CS3, CT3 Asset Pricing Model: Capital Asset Pricing Model, Arbitrage
Pricing Theory.
References:
1. Elandt-Johnson, R. C., & Johnson, N. L. (1999). Efficient market hypothesis
Survival models and data analysis. John Wiley.
2. Benjamin, B., & Pollard, J. H. (1993). The analysis of Assessment:
mortality and other actuarial statistics. Institute and Continuous Assessment: 40%
Faculty of Actuaries. Final Examination: 60%
3. London, Dick (1998). Survival Models and their
Estimation. ACTEX Publications. Medium of Instruction:
4. Peter J. Smith (2002). Analysis of Failure and Survival English
Data. Chapman & Hall.
Humanity Skill:
CS3, CT3
SIQ3001 ACTUARIAL MATHEMATICS I
References:
Survival distributions: lifetime probability functions, force of 1. Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann,
mortality, moments and variance, parametric survival W. N. (2009). Modern portfolio theory and investment
models, percentiles, recursions, fractional ages, select and analysis. John Wiley & Sons.
ultimate life tables. 2. Dobbins, R., Witt, S. F., & Fielding, J. (1994). Portfolio
theory and investment management. 2nd Ed., Wiley-
Life Insurances: continuous type life insurances, discrete Blackwell.
type life insurances, probabilities, percentiles, recursive
formula, m-thly payments, varying insurance.

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